The theoretical development of statistical methodology is progressing in the areas of epidemiological models, multiple comparisons and survival analysis, each of which is applicable to longitudinal studies. The research utilizes Bayesian theory and various regression methods for prospective studies. The methodology created provides original contributions to experimental testing of the simultaneous comparison of specified effects (e.g. treatments against a control or placebo), epidemiological study of disease states, survival or failure analysis of longitudinal data and other longitudinal observations representing growth and other physical changes of humans and animals. Accomplishments in the creative use of Bayesian theory in the area of multiple comparisons will fill a void in the established statistical armamentarium.